Question

Determine whether y varies directly with x. If so, find the constant of variation and write the equation.

Answer 1

Answer:

$y=\frac{-6}{x}$

Constant of variation = -6.  

Step-by-step explanation:      

We have been given a graph and we are asked to determine whether y varies directly with x.

Since we know that directly variation means that when x increases, y increases by the same factor and equation $y=kx$ represents the relation between direct variation, where is k is constant of variation.

We can see from our given graph that as x is increasing y is decreasing, therefore, y does not vary directly with x.

As y decreases when x increases, so y varies inversely with x and the equation of inverse variation is of the form $y=\frac{k}{x}$, where k is a constant of variation.  

Let us find constant of variation using point (-2,3) for our given inversely proportional equation.

$3=\frac{k}{-2}$

Multiplying both sides of our equation by -2 we will get,

$3*(-2)=\frac{k}{-2}*(-2)$

$-6=k$      

Therefore, the constant of variation is -6.

Let us substitute $-6=k$ in inverse proportion to get our equation.

$y=\frac{-6}{x}$

Therefore, the equation $y=\frac{-6}{x}$ represents the given relation in the graph.